汇报标题 (Title)：A Flexible Algorithmic Framework for Nonconvex-Linear Minimax Problems on Riemannian Manifolds (黎曼流形上的非凸线性极幼极大问题的一种矫捷的算法框架)
汇报人 (Speaker)：刘亚锋（中国科学院数学与系统科学钻研院，国际驰名专家）
汇报功夫 (Time)：2024年 12月6日 (周五) 14:00-18:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：徐姿 教授
主办部门：理学院数学系
汇报提要：
Recently, there has been growing interest in minimax problems on Riemannian manifolds due to their wide applications in machine learning and signal processing. Although many algorithms have been developed for minimax problems in the Euclidean setting, relatively few works studied minimax problems on manifolds. In this talk, we focus on the nonconvex-linear minimax problem on Riemannian manifolds. We propose a flexible Riemannian alternating descent ascent algorithmic framework and prove that it achieves the best-known iteration complexity known to date. Various customized simple yet efficient algorithms can be incorporated within the proposed algorithmic framework and applied to different problem scenarios. We also reveal intriguing similarities and differences between the algorithms developed within our proposed framework and existing algorithms, which provide important insights into why the former outperform the latter. Lastly, we report extensive numerical results on sparse principal component analysis (PCA), fair PCA, and sparse spectral clustering to demonstrate the superior performance of the proposed algorithms.
